I would be concerned about the welds holding and subsequent injuries. My experience when welding on tools has not always been good. I think it has to do with the carbon content of the steel, the welds don’t always stay together even though they look good. Keep this in mind when using it if you go this route.

A better way I think would be to insert the thumb ratchet inside the cavity of a one piece handle but this would require significantly more effort.

I would also be concerned about any springs inside the ratchet mechanism, the heat may alter the performance. I would disassemble it before welding.

I doubt the walls of the thumbdrive ratchet head are thick enough to weld on and get good strength without ruining the internals.

I think if I was in a bind and needed to do this I would use a normal ratchet, and then take a piece of flat stock about 14 inches long and drill a hole in the center that is a slip fit over the ratchet handle. Bend the flat stock in a U shape around the ratchet head and the legs of the U will form the opposing handle. Smash them together and weld them into a solid leg if you like.

Alternately you could do the same thing with a shorter piece of flat bar, and just make the U long enough to weld a round bar inbetween the ends. This way you still aren't welding on the ratchet.